Multi-dimensional fractional number of bits modulation scheme

ABSTRACT

A method of encoding information bits of a communication signal for a communication system ( 10 ) is provided. The method includes decomposing the communication signal having a corresponding M 1 -ary modulation constellation into a M 2 -ary constellation, and a M 3 -ary constellation to generate one or more symbols S i . The one or more symbols S i  are mapped using a bit-to-symbol table to generate an encoded communication signal. Decoding methods are also provided for uncoded modulation and trellis coded modulation (TCM). A transmitter ( 20 ) comprising an encoder ( 12 ) for performing TCM that is capable of transmitting a fractional number of information bits per transmitted symbol is also provided.

TECHNICAL FIELD

The present invention relates generally to coded and uncodedcommunication modulation schemes, and more particularly, to a method andsystem for transmitting and receiving a fractional number of bits pertransmission symbol within a communication system.

BACKGROUND OF THE INVENTION

A number of criteria are reviewed when determining effectiveness of acommunication system including: cost, channel bandwidth, requiredtransmitter power, signal-to-noise ratios, probability of bit error,time delay, and other criteria known in the art. In order to satisfy theabove criteria various modulation schemes and coding methods have beendeveloped.

In order to increase bit rate modulation constellations of more than twopoints, such as quadrature amplitude modulation (QAM) and phase shiftkeying (PSK), have been used at the cost of smaller Euclidean distances,distances between adjacent points in a signal constellation. The smallerthe distance between the points the more difficult to decipher betweenadjacent points.

Additionally, coding is used to minimize errors in a receivedcommunication signal. Errors develop through transmission due tocommunication system and environmental effects on the communicationsignal. For example, a binary “1” may be converted to a binary “0” orvice versa in a transmitted communication signal.

One such common coding scheme is channel coding, which introducescontrolled redundancy in order to reduce channel error rates. Asredundant bits are added for coding purposes overall symbol rateincreases for a particular information data rate causing bandwidth toincrease. Another coding scheme, the so-called Trellis-Coded Modulation(TCM), combines modulation and coding to achieve coding gain withoutincreasing bandwidth. Bandwidth efficient trellis-coded modulationschemes are employed to ensure performance of various communicationchannels including satellite channels for higher throughput.

Traditionally, two-dimensional (2-D) TCM employs 2^(m+1) symbols totransmit an information signal containing m information bits per symbol.Each bit corresponding to a possible “0” or “1”. Through coding m+1coded bits are used to transmit m information bits. There are 2^(m+1)possible combinations of zeros and ones per symbol. Thus, the number ofinformation bits m per transmitted symbol is an integer. For example,when transmitting four symbols per communication signal having twoinformation bits per symbol, 12 coded bits are required, three codedbits per symbol. So when a communication system is required to send aninformation signal containing 9 information bits a full additionalsymbol must be used. The downfall to adding additional symbols is thatthe time of the completed transmission increases. If the time of thecompleted transmission is fixed the communication system power andbandwidth requirements will need to be increased to transmit one extrainformation bit. Therefore, the communication system is overbuilt andunder utilized due to additional unused information bits. The additionalrequirements result in an inefficient and cost ineffective communicationsystem.

Unfortunately with traditional TCM schemes, when m increases, codinggain increases more slowly and the error coefficient of the code beginsto dominate performance. As the number of information bits is increasedper symbol, constellations become difficult to create in 2-D.Additionally, cost of utilizing coded 2-D schemes is high, as comparedto uncoded schemes, due to added redundant bits.

Multi-dimensional TCM provides higher coding gain and improvedperformance over 2-D TCM. Multi-dimensional TCM is used to reduce thenumber of redundant bits and constellation sizes and therefore reducethe manufacturing and operating costs. Several multi-dimensional schemeshave been suggested, each having a large amount of constellation pointsin order to transmit a small number of information bits per symbol. Thedesign purpose of the multidimensional schemes is to use additionaldimensions over 2-D schemes to reduce the number of constellationpoints. However, it has been determined that the multidimensionalschemes, although not designed to do so, way be used to transmit afractional number of information bits per symbol.

Transmitting a fractional number of bits per symbol provides anappropriate amount of power and bandwidth for a desired amount oftransmitted information bits and corresponding symbols and improveserror performance. In other words, continuing from the above example thecommunication system may transmit 2.25 information bits per symbol onaverage instead of transmitting an additional symbol. The 2-D TCMfractional number of bits per symbol scheme has been suggested for20-QAM, 24-QAM, 64-QAM, 96-QAM, and 112-QAM constellations. The 2-D TCMfactional number of bits per symbol scheme uses a partition tree tobreakdown an initial constellation, at a top level, into multiplesubsets, each subset having multiple representative constellations. Acertain percentage of constellations in the lowest level subset have afirst amount of uncoded bits and the remaining percentage have a secondamount of uncoded bits. During modulation coded bits equally selectbetween the lowest level subset constellations. Thus, in transmission afractional average number of bits per symbol can be calculated dependingupon the stated percentages.

Since the original design purpose of traditional multi-dimensional TCMmethods was not to modulate a fractional number of bits per symbol,these methods are limited in effectiveness.

It would therefore be desirable to design a communication systemtransmitter and receiver that improves upon the above listed criteriaincluding minimizing bit error rate, system complexity, and powerconsumption and is designed for the purpose of performing TCM for afactional number of bits per symbol.

The goal in designing of a communication system is to minimize costs,channel bandwidth, required transmitter power, probability of bit error,time delay.

SUMMARY OF THE INVENTION

The present invention provides a method and apparatus for transmittingand receiving a fractional number of bits per transmission symbol withina communication system. A method of encoding information bits of acommunication signal for a communication system is provided. The methodincludes decomposing the communication signal having a correspondingM₁-ary constellation into a M₂-ary constellation, and a M₃-aryconstellation to generate one or more symbols S_(i). The one or moresymbols S_(i) are mapped using a bit-to-symbol table to generate anencoded communication signal. Decoding methods are also provided foruncoded modulation and trellis coded modulation (TCM). A transmittercomprising an encoder for performing TCM that is capable of transmittinga fractional number of information bits per transmitted symbol is alsoprovided.

One of several advantages of the present invention is the ability toencode and map multiple symbols simultaneously. In so doing providing aneffective method of transmitting a fractional number of bits per symbol.

Another advantage of the present invention is system versatility andflexibility in that the present invention provides a generalized encodermethod for M-ary QAM and PSK levels including lower QAM levels, forlower consumption and greater communication system efficiency.

Furthermore, the present invention provides a multi-dimensional TCMscheme for transmitting a factional number of bits per symbol that has alow bit error rate and lower energy-per-bit noise density ratio ascomparable to similar level M-ary traditional TCM methods.

The present invention itself, together with attendant advantages, willbe best understood by reference to the following detailed description,taken in conjunction with the accompanying figures.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of this invention reference should nowbe had to the embodiments illustrated in greater detail in theaccompanying figures and described below by way of examples of theinvention wherein:

FIG. 1 is a block diagrammatic view of a satellite communication systemhaving a transmitter encoder and a receiver decoder in accordance withan embodiment of the present invention;

FIG. 2 is a 10-PSK constellation conversion to a 8-QAM constellation anda B-PSK constellation in accordance with an embodiment of the presentinvention;

FIG. 3 is a 10-QAM constellation in accordance with an embodiment of thepresent invention;

FIG. 4 is an uncoded simulation result comparison plot including anuncoded 10-PSK simulation result in accordance with an embodiment of thepresent invention;

FIG. 5 is a logic flow diagram illustrating a method of encodinginformation bits of a communication signal for the communication systemusing uncoded modulation in accordance with an embodiment of the presentinvention;

FIG. 6 is a logic flow diagram illustrating a method of decoding areceived uncoded modulated communication signal in accordance with anembodiment of the present invention;

FIG. 7 is a block diagrammatic view of a multidimensional TCMtransmitter encoder in accordance with an embodiment of the presentinvention;

FIG. 8 is an uncoded and coded TCM comparison simulation result plotincluding a coded 10-QAM TCM simulation result in accordance with anembodiment of the present invention;

FIG. 9 is a logic flow diagram illustrating another method of encodinginformation bits of a communication signal for the satellitecommunication system using coded TCM in accordance with an embodiment ofthe present invention; and

FIG. 10 is a logic flow diagram illustrating a method of decoding areceived coded TCM communication signal in accordance with an embodimentof the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

In each of the following figures, the same reference numerals are usedto refer to the same components. While the present invention isdescribed with respect to a method and apparatus for transmitting andreceiving a fractional number of bits per transmission symbol within acommunication system, the present invention may be adapted to be used invarious systems including: satellite systems, ground based systems,telecommunication systems, mobile systems, aeronautical systems, andvarious other communication systems.

In the following description, various operating parameters andcomponents are described for one constructed embodiment. These specificparameters and components are included as examples and are not meant tobe limiting.

Also, in the following description the terms “communication signal” mayrefer to any signal transmitted or received in a communication system. Acommunication signal may be an encoded communication signal, a modulatedsignal, a serial interchange signal, an input or an output signal, orany other communication signal known in the art.

Referring now to FIG. 1, a block diagrammatic view of a satellitecommunication system 10 having a transmitter encoder 12 and a receiverdecoder 14 in accordance with an embodiment of the present invention, isshown. A satellite 16 includes a digital source 18 electrically coupledto the transmitter encoder 12 of a transmitter 20. The encoder 12converts a digital source communication signal into Inphase-Quadrature(I-Q) signals I(t) and Q(t). The transmitter encoder 12 is alsoelectrically coupled to an I-Q modulator 22, which convert the I-Qsignals I(t) and Q(t) into a modulated signal s(t). The modulated signals(t) is transmitted over a transmission medium 24 to an I-Q demodulator26 of ground station 28. The transmission medium 24 converts themodulated signal s(t) into transmission medium signal or received signalr(t). A(t) is equal to modulated signal s(t) plus a noise signal n(t).The I-Q demodulator 26 converts the received signal r(t) into a modifiedI-Q signals I′(t) and Q′(t). The I-Q demodulator 26 is electricallycoupled to the decoder 14 of a receiver 30. The decoder converts themodified I-Q signals I′(t) and Q′(t) into a decoded signal, which isreceived by a digital sink 32.

Referring now to FIG. 2, a decomposition from a 10 phase shift keying(PSK) constellation 40 to an 8 quadrature amplitude modulation (QAM)constellation 42 and a binary (B)-PSK constellation 44 in accordancewith an embodiment of the present invention, is shown. The 10-PSKconstellation 40 has 10 points 46 corresponding to various phases of acommunication signal. Points having coordinates (−1,0) and (1,0) areremoved from the 10-PSK constellation to form the B-PSK constellation.Although, not illustrated each point 48 in the 8-AM constellation mayalso have varying amplitude. The 10-PSK constellation 40 is intended forillustration purposes only, any M₁-ary constellation may be decomposedinto an M₂-ary constellation and a M₃-ary constellation.

Referring now to FIG. 3, a 10-QAM constellation 50 in accordance with anembodiment of the present invention, is shown The 10-QAM constellation50 is similar to the 8-QAM constellation and the B-PSK constellationshown in FIG. 2 except for amplitude differences in points 52, eachhaving an amplitude of two in stead instead of one. Points 54 located ona unit circle 56 are referred to as inner points corresponding to atleast one inner symbol. Point 52, having coordinates (−2,0) and (2,0)are referred to as outer points and correspond to at least one outersymbol. The 10-QAM constellation has 2^(m) inner symbols and 2^(x) outersymbols, where m is equal to tree and x is equal to one. The 10-QAMconstellation is also for illustration purposes only. Any M₁-aryconstellation may be decomposed into an M₂-ary constellation and anM₃-ary constellation, where M₁ is equal to the total number of points 52and 54, M₂ is equal to 2^(m), and M₃ is equal to 2^(x).

Referring now to FIG. 4, an uncoded simulation result comparison plotincluding an uncoded 10-PSK simulation result in accordance with anembodiment of the present invention, is shown. Corresponding symbolerror rate (SER) versus energy-per-bit/noise-density ratio (Es/No)curves for a traditional uncoded 8-PSK modulation scheme, a traditionaluncoded 16-PSK modulation scheme, and the uncoded 10-PSK modulationscheme of the present invention, are shown. Curve 64 corresponds withthe traditional uncoded 8-PSK modulation scheme. Curve 62 correspondswith the traditional uncoded 16-PSK modulation scheme. Curve 60corresponds with the uncoded 10-QAM modulation scheme of the presentinvention.

When transmitting an additional information bit over the 8-PSKmodulation scheme, traditionally, a 16-PSK modulation scheme wasrequired. Note that there is a 5.8 db penalty between curve 60 and 62 atSER=10ˆ−4. Using the uncoded 10-QAM modulation scheme of the presentinvention a 1.5 db increase occurs over the traditional 8-PSK modulationscheme, since 3.25 information bits per symbol are transmitted ratherthan 4 information bits per symbols as with the uncoded 16-PSKmodulation scheme. The uncoded 10-PSK modulation scheme is furtherexplained and generalized in the method shown in FIG. 5.

Referring now to FIGS. 1 and 5, in FIG. 5 a logic flow diagramillustrating a method of encoding information bits of a communicationsignal for the satellite communication system 10 using uncodedmodulation in accordance with an embodiment of the present invention, isshown.

In step 70, encoder 12 groups m·2^((m−x))+1 information bits, where x=1,2, 3, . . . , m−1. The encoder receives a series of information bits andconverts the series of information bits into m·2^((m−x))+1 parallelinformation bit groups.

In step 72, the encoder generates 2^((m−x)) symbol constellations,having 2^((m−x)) symbols, such that there is m+(½)^((m−x)) informationbits per symbol.

In step 72 a, encoder 12 decomposes the communication signal having acorresponding M₁-ary constellation into an M₂-ary constellation and aM₃-ary constellation to generate a symbol series containing one or moresymbols S_(i) in a specified order, where i=1, 2, 3, . . . The encoder12 uses 2^(m)+2^(x)ary symbol constellations when decomposing thecommunication signal. So for the 10-PSK constellation 40 there are foursymbols, each of which having either one or three information bits forB-PSK and S-QAM constellations, respectively.

In step 72 b, the one or more symbols S_(i) are mapped, using abit-to-symbol mapping rule in table 1, to generate an encodedcommunication signal. TABLE 1 Bits-to-Symbol Mapping Rule for Uncoded10-PSK Constellation Position bits Communication Signal having S_(i)Symbols bit I₁₃ I₁₁ I₁₂ S₁ S₂ S₃ S₄ 0 0 or 1 0 or 1

Constellation Type 8QAM 8QAM 8QAM 8QAM Information Bits I₁, I₂, I₃ I₄,I₅, I₆ I₇, I₈, I₉ I₁₀, I₁₁, I₁₂ 1 0 0

Constellation Type BPSK 8QAM 8QAM 8QAM Information Bits I₁ I₂, I₃, I₄I₅, I₆, I₇ I₈, I₉, I₁₀ 1 0 1

Constellation Type 8QAM BPSK 8QAM 8QAM Information Bits I₁, I₂, I₃ I₄I₅, I₆, I₇ I₈, I₉, I₁₀ 1 1 0

Constellation Type 8QAM 8QAM BPSK 8QAM Information Bits I₁, I₂, I₃ I₄,I₅, I₆ I₇ I₈, I₉, I₁₀ 1 1 1

Constellation Type 8QAM 8QAM 8QAM BPSK Information Bits I₁, I₂, I₃ I₄,I₅, I₆ I₇, I₈, I₉ I₁₀

In step 72 c, if constellation bit is “1” then one symbol in 2^((m−n))symbols is assigned to have one or more position bits. For the 10-PSKexample, I₁₃ is constellation bit and (I₁₁,I₁₂) are position bitscorresponding with a B-PSK symbol position in a symbol series (4symbols).

In step 72 d, one constellation bit is represented by 2^((m−x)) symbols.All symbols in a symbol series (2^((m−x)) symbols) are M₂-ary symbols(inner symbols) if the constellation bit is a “0”. One symbol in asymbol series (2^((m−x)) symbols) is an M₃-ary symbol (outer symbol) ifthe constellation bit is a “1”. So for example, using the 10-PSK schemeof the present invention, I₁₃ is a constellation bit determinative ofwhether a symbol series is corresponding with the 8-QAM constellation 42or the B-PSK constellation 44. In the first row of Table 1, since I₁₃ iszero all symbols correspond with an 8-QAM constellation. In rows 2-5 ofTable 1, since I₁₃ is one a B-PSK constellation corresponding symbolexists in each row.

The above-described steps are meant to be an illustrative example, thesteps may be performed synchronously or in a different order dependingupon the application.

Referring now to FIGS. 1 and 6, a logic flow diagram illustrating amethod of decoding a received uncoded modulated communication signal inaccordance with an embodiment of the present invention, is shown.

In step 80, the decoder 14 receives the modified I-Q signals I′(t) andQ′(t).

In step 82, the decoder 14 denotes the modified I-Q signals I′(t) andQ′(t) into one or more symbols S_(i) by grouping 2^((m−x)) receivedsymbols. For 10-PSK there are four symbols S₁, S₂, S₃, and S₄.

In step 84, one or more distances d_(M2-ary) ¹ and one or more distancesd_(M3-ary) ¹ for each of the one or more symbols S_(i) are determined,using methods known in the art, where i=1, 2, 3, . . . , 2^((m−x)).

In step 86, one or more distance totals D_(h), for one or more possiblesymbol series (2^((m−x)) symbols), in response to the one or moredistances d_(M2-ary) ¹, and at most one d_(M3-ary) ¹ are determined,where h=0, 1, 2, . . . 2^((m−x)). For the 10-PSK example the followingis the known possible distance totals D_(h):D ₀ =d ¹ _(BQAM) +d ² _(8QAM) +d ³ _(8QAM) +d ⁴ _(8QAM),D ₁ =d ¹ _(BQAM) +d ² _(8QAM) +d ³ _(8QAM) +d ⁴ _(BQAM),D ₂ =d ¹ _(8QAM) +d ² _(BQAM) +d ³ _(8QAM) +d ⁴ _(8QAM),D ₃ =d ¹ _(8QAM) +d ² _(8QAM) +d ³ _(BQAM) +d ⁴ _(8QAM),D ₄ =d ¹ _(8QAM) +d ² _(BQAM) +d ³ _(8QAM) +d ⁴ _(BQAM),

In step 88, a distance total D_(I-Q) for the modified I-Q signals I′(t)and Q′(t) is determined. D_(I-Q) is the minimum distance from the set ofdistance totals D_(h) above. The information bits corresponding to the2^(m-x) symbols represented by D_(I-Q) become the decoded communicationsignal.

In step 90, the decoder 14 outputs the decoded communication signal.

Referring now to FIG. 7, a block diagrammatic view of amulti-dimensional TCM transmitter encoder 100 in accordance with anembodiment of the present invention, is shown. The encoder 100 mayreplace the encoder 12 from above in FIG. 1. The encoder 100 includes aswap controller 102, a padder 104, a convolutional encoder 106, and asignal set mapper 108. A communication signal is inputted into a firstserial-to-parallel converter 110, which is electrically coupled to theswap controller 102, where the communication signal is received. Theswap controller 102 appropriately positions symbols within thecommunication signal in conjunction with the padder 104, which insertsredundant bits into the communication signal. The swap controller 102 iselectrically coupled to the padder 104 via a parallel-to-serialconverter 112. The convolutional encoder 106 is electrically coupled tothe padder 104 via a second serial-to-parallel converter 114. Theconvolutional encoder 106 is also electrically coupled to and operatesin conjunction with the signal set mapper 108 to map the communicationsignal into modulated I-Q signals I(t) and Q(t). The padder 104 may be asolid-state stand-alone device or may be part of another device such asthe swap controller 102.

The swap controller 102 is preferably microprocessor-based such as acomputer having a central processing unit, memory 115 (RAM and/or ROM),and associated input and output buses. The swap controller 102 may be aportion of a central control unit or may be a stand-gone component. Theswap controller 102 determines whether there is to be an outer symbol inthe communication signal, and when there is an outer symbol, where theouter symbol is to be positioned relative to inner symbols within thecommunication signal. This is further explained in more detail below.

The convolutional encoder 106 includes multiple convolutional encoderchannels 116. At least one convolutional encoder channel 116 has aredundant circuit 118. The redundant circuit 118 includes at least oneredundant channel 120 having multiple delay components 122 and afeedback loop 124. The feedback loop 124 is electrically coupled to aredundant channel output 126 with a delay component F₃. Redundant bitsreceived from the padder 104 are indicative of when to transmit an outersymbol. For the 10-QAM TCM example the convolutional encoder 106 hasthree input channels A₁-A₃, four output channels B₁-B₄, and three delaycomponents F₁-F₃.

The signal set mapper 108 may also be a solid-state stand-alone deviceor may be part of another device such as the swap controller 102. Thesignal set mapper 108, for the 10-QAM example, has four input channelscoinciding with the four output channels of the convolutional encoder106, which are B₁-B₄. The signal set mapper also has two output channelsC₁ and C₂. Note that each bit received from the secondserial-to-parallel converter 114 within a communication signal issimultaneously coded by the convolutional encoder 106 and signal setmapper 108, unlike convolutional encoders of prior art.

Referring now to FIG. 8, an uncoded and coded TCM comparison simulationresult plot including a coded 10-QAM TCM simulation result in accordancewith an embodiment of the present invention, is shown. Corresponding biterror rate (BER) versus energy-per-bit/noise-density ratio (Es/No)curves for a traditional uncoded Q-PSK modulation scheme, a traditionaluncoded 8-PSK modulation scheme, a traditional coded 8-PSK modulationscheme, a traditional coded 16-PSK modulation scheme, a traditionalcoded 16-QAM modulation scheme, and a coded 10-QAM modulation scheme ofthe present invention. Curve 130 corresponds with the traditionaluncoded Q-PSK modulation scheme. Curve 138 corresponds with thetraditional coded 8-PSK modulation scheme. Curve 134 corresponds withthe traditional coded 16-PSK modulation scheme. Curve 136 correspondswith the traditional coded 16-QAM modulation scheme. Curve 132corresponds with a 10-QAM modulation scheme of the present invention.2.25 information bits per symbol are transmitted using the 10-QAM schemeof the present invention transmitting, with a resulting Es/No=10.8 db atBER=10⁻⁴.

Referring now to FIGS. 7 and 9, a logic flow diagram illustratinganother method of encoding information bits of a communication signalfor the satellite communication system 10 using coded TCM in accordancewith an embodiment of the present invention, is shown in FIG. 9.Modulated I-Q signals I(t) and Q(t) are generated to havem−1+(½)^((m−x )) information bits per symbol where x=1, 2, 3, . . . ,m−1.

In step 150, the first serial-to-parallel converter 110 converts aninput signal 151 into a first parallel signal 152, by grouping(m−1)·2^((m−x))+1 information bits into parallel information bit groups.The first parallel signal 152 for the 10-QAM scheme has nine channelscorresponding to nine information bits a₁ . . . , a₉ that are containedwithin the input signal 151.

In step 154, the swap controller 102 swaps order of information bits inthe first parallel signal 152 to generate a parallel interchange signal156. For the 10-QAM example, bit 7 is a constellation bit and bits 8 and9 are position bits, as shown in Table 2, which is stored in swapcontroller memory 115. When bit 7 is equal to 0 then no bits areswapped. When bit 7 is equal to a 1 then position bits 8 and 9 determinewhich bits are swapped. TABLE 2 Bits-to-Symbol Mapping Rule forTrellis-coded 10-QAM Constellation Position bits Communication Signalhaving S_(I) Symbols bit a₇ a₈ a₉ S₁ S₂ S₃ S₄ 0 0 or 1 0 or 1

coded symbol IS IS IS IS Information Bits a₁, a₂ a₃, a₄ a₅, a₆ 0, a₈, a₉1 0 0

coded symbol OS IS IS IS Information Bits 1, 0, 0 a₃, a₄ a₅, a₆ a₁, a₂ 10 1

coded symbol IS OS IS IS Information Bits a₁, a₂ 1, 0, 1 a₅, a₆ a₃, a₄ 11 0

coded symbol IS IS OS IS Information Bits a₁, a₂ a₃, a₄ 1, 1, 0 a₅, a₆ 11 1

coded symbol IS IS IS OS Information Bits a₁, a₂ a₃, a₄ a₅, a₆ 1, 1, 1

In step 158, a parallel-to-serial converter 112 converts the interchangesignal 156 into a serial interchange signal 160. The converter 112receives m−1+(½)^((m−x)) information bits and one bit at a time isoutputted from the converter 112.

In step 162, the padder 104 pads the serial interchange signal 160 withredundant bits to generate a padded interchange signal 164. The swapcontroller 102 may be electrically coupled to the padder 104 andgenerate a position signal. In response to the position signal thepadder 104 pads the interchange signal 160 with zeros, as illustrated inTable 3. The singe asterisk* cells in Table 3 are redundant bits. Thedouble asterisk** cells in Table 3 are constellation bit. The tripleasterisk*** cells in Table 3 are position bits. TABLE 3 IllustratingRedundant Bit Padding for 10-QAM Output Symbol Symbols Series OptionsPadder S₁ S₂ S₃ S₄ 1 input a₁ a₂ a₃ a₄ a₅ a₆ 0** a₈ a₉ output 0* a₁ a₂0* a₃ a₄ 0* a₅ a₆ 0** a₈ a₉ 2 input 1** 0*** 0*** a₃ a₄ a₅ a₆ a₁ a₂output 1** 0*** 0*** 0* a₃ a₄ 0* a₅ a₆ 0* a₁ a₂ 3 input a₁ a₂ 1** 0***1*** a₅ a₆ a₃ a₄ output 0* a1 a₂ 1** 0*** 1*** 0* a₅ a₆ 0* a₃ a₄ 4 inputa₁ a₂ a₃ a₄ 1** 1*** 0*** a₅ a₆ output 0* a₁ a₂ 0* a₃ a₄ 1** 1*** 0***0* a₅ a₆ 5 input a₁ a₂ a₃ a₄ a₅ a₆ 1** 1*** 1*** output 0* a₁ a₂ 0* a₃a₄ 0* a₅ a₆ 1** 1*** 1***

In step 166, the second serial-to-parallel converter 114 converts thepadded interchange signal 164 into a convolutional encoder input signal168. One information bit is inputted into the converter 114 at a timeand m information bits are outputted from the converter 114.

In step 170, the convolutional encoder 106 codes the convolutionalencoder input signal 168 to generate a convolutional encoder outputsignal 172 containing additional redundant bits from redundant channel120. m information bits are inputted into the convolutional encoder 106and m+1 information bits are outputted from the convolutional encoder106. Table 4 illustrates a first 8 cases of 64 possible cases of theconvolutional encoder 106, for the 10-AM scheme. TABLE 4 SampleConvolutional Encoder States for 10-QAM Convolutional Encoder Old statesof New states of Input bits Delay Components Delay Components Outputbits A₃ A₂ A₁ F₃ F₂ F₁ F₃ F₂ F₁ B₄ B₃ B₂ B₁ 0 0 0 0 0 0 0 0 0 0 0 0 0 00 1 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 1 1 0 11 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 1 0 1 0 1 1 0 0 0 0 0 10 1 1 0 0 1 1 1 0 0 0 0 1 1 1 1 1 0

In step 174, the signal set mapper 108 maps the convolutional encoderoutput signal 172 to generate the I-Q signals I(t) and Q(t), as shown inTable 5. The mapper 108 receives (m−1)·2^((m−x))+1 information bits andoutputs 2^((m−x)) symbols, such that there are m−1+(½)^((m−x))information bits per symbol. As in steps 70-70 d described with respectto FIG. 5 above, the mapper 108 uses 2^(m)+2^(x)ary constellations whenforming 2^(m)-ary inner symbols and 2^(x)-ary outer symbols. The twooutput channels C₁ and C₂ form the I-Q signals I(t) and Q(t),respectively. Table 5 illustrates mapping of all 64 possibleconvolutional encoder input states to signal set mapper output states.Each column in Table 5 represents three bits. So for example, the firstcase in Table 4 where A1-A3 all have a value of 0 corresponds with row1, column 1 of Table 5. Also, the convolutional encoder input symbol andsignal set mapper output symbol columns are doubled for delay componentstates that repeat. So in row 1, the convolutional encoder input firstcase and fifth case are shown having the same delay component states andrespective signal set mapper output states. TABLE 5 Sample ConvolutionalEncoder and Signal Set Mapper States for 10-QAM Coded TCM SchemeConvolutional Old State New State Signal set Encoder Input of Delay ofDelay Mapper Output Symbol Components Components Symbol 0 4 0 0 0 8 1 50 1 2 8 2 6 0 2 4 9 3 7 0 3 6 9 0 4 1 4 1 8 1 5 1 5 3 8 2 6 1 6 5 9 3 71 7 7 9 0 4 2 1 0 8 1 5 2 0 2 8 2 6 2 3 4 9 3 7 2 2 6 9 0 4 3 5 1 8 1 53 4 3 8 2 6 3 7 5 9 3 7 3 6 7 9 0 4 4 2 0 8 1 5 4 3 2 8 2 6 4 0 4 9 3 74 1 6 9 0 4 5 6 1 8 1 5 5 7 3 8 2 6 5 4 5 9 3 7 5 5 7 9 0 4 6 3 0 8 1 56 2 2 8 2 6 6 1 4 9 3 7 6 0 6 9 0 4 7 7 1 8 1 5 7 6 3 8 2 6 7 5 5 9 3 77 4 7 9

In step 174 a, the signal set mapper 108 decomposes the convolutionalencoder output signal 172 having a corresponding M₁-ary constellationinto a M₂-ary constellation, and a M₃-ary constellation to generate oneor more symbols S_(i), where M₂ is 2^(m) inner points and M₃ is 2^(x)outer points. The M₁-ary constellation may be a PSK constellation or aQAM constellation.

In step 174 b, the one or more symbols S_(i) are mapped using abit-to-symbol mapping rule illustrated in Table 2, above, which isstored in signal set mapper memory 175 to generate an encodedcommunication signal.

In step 174 c, the signal set mapper 108 assigns at least one symbol ofsymbols S_(i) to have one or more constellation bits, m−x position bits,and x−1 point bits. The constellation bits are indicative of whether thecommunication signal corresponds to the M₂-ary constellation or theM₃-ary constellation. The swap controller 102 assigns (m−1)·(2^(m−x))+1information bits to 2^(m−x) inner symbols or to 2 ^(m−x)−1 inner symbolsand one outer symbol in response to the constellation bit being a ‘0’ ora ‘1’, respectively. The position bits are indicative of one outersymbol positions. The symbols S_(i) are repositioned in response to them−x position bits. The point bits are indicative of an outer pointconfiguration that has a minimum distance d_(free), minimum distancebetween points. The outer symbol is selected from 2^(x)-ary to maximizethe minimum distance d_(free) to minimize bit error. As for a moredetailed understanding of d_(free) “Error Control Coding: Fundamentalsand Applications”, by Shu Lin and Daniel J. Costelo, Jr. is incorporatedherein by reference.

Referring now to FIG. 10, a method of decoding information bits for acommunication system that uses the coded TCM scheme of the presentinvention, is shown.

In step 180, the decoder 14 receives the modified I-Q signals I′(t) andQ′(t), similar to step 80 above. A series of symbols are obtained.

In step 182, the decoder 14 denotes the modified I-Q signals I′(t) andQ′(t) into multiple symbols S_(i), similar to step 82 above.

In step 184, the decoder 14 decodes the multiple symbols S_(i)simultaneously and outputs information bits corresponding to thesymbols. For further decoding algorithm detail see Viterbi decodingalgorithm described in “Error Control Coding: Fundamentals andApplications”, by Shu Lin and Daniel J. Costelo, Jr., which isincorporated herein by reference.

The present invention therefore provides a generalized uncoded and codedmulti-dimensional modulation schemes that are designed for transmissionof a fractional number of bits per symbol. The present invention, indoing so, has provided a flexible communication system with minimumoperating power consumption, decreased bit error, and minimumsignal-to-noise ratios.

The above-described apparatus, to one skilled in the art, is capable ofbeing adapted for various purposes and is not limited to the followingsystems: satellite systems, ground based systems, telecommunicationsystems, mobile systems, aeronautical systems, and various othercommunication systems. The above-described invention may also be variedwithout deviating from the spirit and scope of the invention ascontemplated by the following claims.

1-19. (canceled)
 20. A method of decoding information bits for acommunication system that uses trellis-coded modulation comprising:receiving a modified I-Q signals; denoting said modified I-Q signalsinto a plurality of symbols S_(i); and decoding said plurality ofsymbols S_(i) simultaneously